Timeline for Can you prove and/or generalize this formula involving the Möbius function at n = square free numbers for elliptic curve related sequence in the OEIS?
Current License: CC BY-SA 4.0
15 events
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| Oct 18, 2023 at 16:30 | comment | added | Chris Wuthrich | I am not sure why you keep updating this. Max and my comment solved the initial question. I doubt many people will want to follow your coding experiments without extra motivation or explanations. (But if there is, maybe a new question is better than adding to this). | |
| Oct 18, 2023 at 14:02 | history | edited | Mats Granvik | CC BY-SA 4.0 |
Added convolution.
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| Oct 16, 2023 at 15:12 | history | edited | Mats Granvik | CC BY-SA 4.0 |
added 1832 characters in body
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| Oct 10, 2023 at 18:46 | history | edited | Mats Granvik | CC BY-SA 4.0 |
Changed question to be about square free numbers instead of only primes.
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| Oct 10, 2023 at 18:41 | history | edited | Mats Granvik | CC BY-SA 4.0 |
Changed question to be about square free numbers instead of only primes.
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| Oct 10, 2023 at 8:58 | comment | added | Chris Wuthrich | .. and that is true as the modular form associated to this elliptic curve of conductor 11 is an eta quotient. I believe this is the contents of the article by Shimura linked in the oeis. | |
| Oct 9, 2023 at 21:49 | comment | added | Max Alekseyev | Since $p_n$ is prime, $\gcd$ can take only 2 values: 1 or $p_n$. Then the conjecture is reduced to just saying that the order of the elliptic curve $y^2+y=x^3-x^2$ over the field $\mathbb{F}_{p_n}$ equals $$p_n + 1 - \texttt{A002070}(n).$$ | |
| Oct 9, 2023 at 21:22 | history | edited | Max Alekseyev | CC BY-SA 4.0 |
corrected according to the comment
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| Oct 9, 2023 at 18:10 | comment | added | Mats Granvik |
(*start*)nn = 15;(*set nn=12 for faster computation*)f = x^3 - x^2 - y^2 - y; g[n_] := DivisorSum[n, MoebiusMu[#] # &]; Monitor[ Table[Sum[ Sum[Sum[If[GCD[f, Prime[n]] == k, 1, 0]*g[k]/Prime[n], {x, 1, Prime[n]}], {y, 1, Prime[n]}], {k, 1, Prime[n]}], {n, 1, nn}], n] (*end*)
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| Oct 9, 2023 at 18:02 | comment | added | Mats Granvik | The correct form is probably: $$A002070(n) = \sum _{k=1}^{p_n} \left(\sum _{y=1}^{p_n} \left(\sum _{x=1}^{p_n} \frac{g(k) \left[\gcd (f(x,y),p_n)=k\right]}{p_n}\right)\right)$$ without the extra $g()$ around $\gcd ()$ and $k$. | |
| Oct 9, 2023 at 17:21 | comment | added | Mats Granvik | Related: math.stackexchange.com/q/4750904/8530 | |
| Oct 9, 2023 at 16:11 | comment | added | Mats Granvik | Should I post this on Mathematics stack exchange instead? | |
| Oct 9, 2023 at 16:01 | history | edited | Mats Granvik | CC BY-SA 4.0 |
edited title
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| Oct 9, 2023 at 15:58 | comment | added | Mats Granvik | If someone knows how to tag this better you are welcome. | |
| Oct 9, 2023 at 15:56 | history | asked | Mats Granvik | CC BY-SA 4.0 |